PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 401

F10 =10*sin(w*tau10/2)./(w*tau10/2);

subplot(3,1,1)

plot(w,F1);

ylabel(‘Amplitude’);

title(‘Spectrum of pulse with tau=1’);

axis([-10 10 -1 2]);

subplot(3,1,2);plot(w,F5);

ylabel(‘Amplitude’);

title(‘Spectrum of pulse with tau=5’);

axis([-7 8 -4 6]);

subplot(3,1,3);plot(w,F10);

xlabel(‘frequency w (in rad/sec)’);

ylabel(‘Amplitude’);

title(‘Spectrum of pulse with tau=10’);

axis([-10 10 -4 11]);

The script fi le square_FT_num is executed and the results are as follows (Figure 4.50):

>> square _ FT _ num

frequency w (in rad/sec)

frequency w (in rad/sec)

(Numerical solutions)

Spectrum of pulse with τ = 1

2

0

6

4

2

− 2

− 4

0

1

− 1

− 10

10

5

0

− 8 − 6

− 6

− 10 − 8 − 6 − 4 − 202

− 4

− 4

− 2

− 2

0

0

2

2

4

4

6

6

8

8

10

Spectrum of pulse τ = 5

Spectrum of pulse τ = 10

frequency w (in rad/sec)

4 6810

Amplitude

Amplitude

Amplitude

FIGURE 4.50

Numerical plots of part 2 of Example 4.8.